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Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

This instrument consists of a wooden base to which a flat rectangular scale printed on white celluloid is attached. The scale is divided logarithmically and arranged in 20 parallel lines. Each line is about five inches long. A wooden frame slides backward and forward over the base. Within this frame is a second frame, which has a clear celluloid window. Four index marks are drawn on the window. A loose metal wedge with a pin attached serves as a pointer, and it may be placed at any point on the window. The scales are marked: THE COOPER 100 INCH SLIDE RULE (/) PATENTED.

The feet of the base are lined with green felt. The instrument fits in a leather-covered cardboard box that is lined with white felt. A sticker inside the lid reads: WILLIAM DUBILIER (/) 72 Esplanade (/) NEW ROCHELLE, N. Y. There is also a note that reads: TELEPHONE, PARK 1081. (/) WIRELESS CALL, 5AU. (/) 94, ADDISON ROAD (/) KENSINGTON, W. 14. (/) 24/12/22 (/) To W. D. (/) With very best wishes for (/) Xmas and the New Year. (/) W.v.P.

William Dubilier (1888–1969), the donor of this instrument, was an American electrical engineer and inventor who received this instrument from a friend in Great Britain in 1922. By 1923, W. F. Stanley & Co. made this rule and stamped the outer frame with its mark. Although the rule worked well for multiplication and percentage problems, it was difficult to set the rule accurately for more complex calculations. At the relatively high price of £4, the instrument probably never sold widely. No patents for the device have been found. For the instruction manual, see MA*259739.01.

Polyhedra in which all faces are equilateral triangles are called deltahedra. The regular tetrahedron, octahedron, and icosahedron are the simplest deltahedra. It also is possible to replace each face of a regular dodecahedron with a “dimple” having five equilateral triangles as sides. This is a model of such a surface. It also may be considered as one of the polyhedra formed by extending the sides of—or stellating—a regular icosahedron.

This deltahedron is folded from paper and held together entirely by hinged folds along the edges. Fifteen of the sixty faces have photographs of students of A. Harry Wheeler at North High School in Worcester, Massachusetts. All are boys. Another face reads: 1927 (/) Stanley H. Olson. A seventeenth face reads: Royal Cooper. Cooper is also shown on one of the sides with a photograph. There is a photograph of Lanley S. Olson, but not Stanley H. Olson. Yet another face of the model has a pencil mark that reads: June – 1927.

From ancient times, bureaucrats have kept numerical records of people and property. Those working for the Inca emperor in 16th-century Peru recorded data on arrangements of knotted strings known as quipus. The devices may also have been used as aids to memory in recounting histories of Inca exploits—the Incas had no written language.

Particularly from the 1880s, collections in South America, Europe, and the United States began to include quipus, usually recovered from the graves of makers or users. The devices were of great interest to historian of mathematics Leslie Leland Locke, a charter member of the Mathematical Association of America. Locke (1875–1943), a native of Grove City, Pennsylvania, received his A.B. from Grove City College in 1896 and his M.A. in 1900. He studied further at Pennsylvania State University, Cornell University, and Columbia. He came to Brooklyn to teach at Adelphi College and then worked from 1908 to 1933 at Maxwell Training School for Teachers, later moving to Brooklyn Technical High School. He also taught in the evening session at Brooklyn College.

Around 1909, while studying under historian of mathematics David Eugene Smith at Teacher’s College of Columbia, Locke became interested in the quipu. He examined several examples at the American Museum of Natural History in detail. In a 1912 paper, Locke argued that the knots on the strings of a quipu represented the decimal digits of numbers, arranged vertically by place value. He extended this research in this volume, published by the American Museum of Natural History in 1923. It includes excerpts of numerous early Spanish and other European texts relating to the quipu, and lists forty-five surviving examples. Locke deemed five of these modern or spurious. He obtained and published illustrations of over thirty of the objects, laying the foundation for further studies.

Locke also took great interest in more modern innovations in computing, particularly the calculating machine. He inscribed and presented this copy of his book to Dorr E. Felt, the head of Felt & Tarrant Manufacturing Company. Felt had invented, and Felt & Tarrant manufactured, the Comptometer, a leading adding machine of its day. The book, along with the rest of Felt’s library relating to the history of mathematical instruments, was given to the Smithsonian Institution by Victor Comptometer Corporation, the successor to Felt & Tarrant.

In addition to joining the MAA when it was established, Locke was a charter member of the History of Science Society and active in the National Council of Teachers of Mathematics.

References:

Marcia Ascher and Robert Ascher, Mathematics of the Incas: Code of the Quipu, Mineola, New York: Dover, 1997. This is a corrected republication of the book Code of the Quipu: A Study in Media, Mathematics, and Culture, published in 1981 by the University of Michigan Press.

Stefanie Gaenger. Relics of the Past: The Collecting and Study of pre-Columbian Antiquities in Peru and Chile,1837–1911, Oxford: Oxford University Press, 2014, esp. 101–159.

A stellation of a regular polyhedron is a polyhedron with faces formed by extending the sides of the faces of the regular polyhedron. Extending the triangular sides of an icosahedron can produce a variety of complex polyhedra, including this one. The surface has sixty short three-sided spikes. These meet in groups of three—each meeting point might be considered as the vertex of a circumscribing regular dodecahedron.

The model is cut and folded from paper. It is Wheeler’s model 382, and number I21 in his series of icosahedra. Wenninger calls the surface the fifteenth stellation of the icosahedron.

Joining points along the radius of two circles generates a family of straight lines. If the circles are at their maximum separation, the lines form a cylinder. When rotated, the circles approach and the surface becomes a hyperboloid of one sheet. Further rotation (not possible on this model) yields a double cone.

String models with elegant brass frames sold for engineering and mathematics education sold from the nineteenth century (see 1985.0112.009). Philip Malmberg, a high school student of A. Harry Wheeler, made this inexpensive version of the surface. He used disks cut from a cardboard box, leftover spools from thread, a wooden dowel, a bit of wire, and thread. Census records indicate that Malmberg went on to work as a draftsman.

This gray-green manually operated ten-key printing adding machine has two rows of white plastic number keys, including complementary numbers for subtraction. There are multiply and non-add keys on the left, and backspace and subtract keys on the right.

The multiply key acts like a repeat key - multiplication is strictly by repeated addition. The place indicator is above the keyboard, with a metal correction key to the left of it. Above and to the right are release, total, and subtotal keys. The printing mechanism and “4”” carriage are toward the back. The ribbon is black. The non-print key is next to the ribbon.

There is a place for a 2-1/2” paper tape, but no paper tape. Above the platen is a serrated edge to tear the paper. A zero value appears before a total. The metal crank with wooden handle is on the right. There are metal feet, but no evidence of any rubber padding.

The machine is marked on the front: Dalton (/) ADDING, (/) LISTING AND (/) CALCULATING MACHINE. The serial number below the crank is: NO170913.

This example came to the Smithsonian from Immaculata School in Washington, D. C.

Compare to MA*333874 and MA*333402.

This closely resembles the Model 181-4 machine described in The Business Machines and Equipment Digest, about. 1928, Sec 3-1, p. 14, 19. This was the “Special $100 Machine.”

This full-keyboard, non-printing manually operated pinwheel calculating machine has a metal frame painted black and nine columns of plastic keys, with three columns black, three columns white, and three more columns black. At the base of each bank of keys is a red clearance key. The underlying keyboard is painted green. Metal rods between banks of keys serve as decimal markers.

Right of the number keys is a red keyboard clearance key, a multiply/divide key, and an addition/subtraction key. The operating crank on the right rotates backward (clockwise) for addition and multiplication and forward (counterclockwise) for subtraction and division.

Behind the keyboard is a movable carriage with the 18 windows of the result register. A lever at the front of the machine shifts the carriage, a button on the right side releases it, and a crank on the left end of the carriage clears it. Behind and above the carriage are nine windows showing digits entered, a lever that can be set for multiplication or division, and nine windows for the revolution register. Rotating a small crank on the right side clears this register.

Decimal markers slide on metal rods above all three registers. A metal flange below the result register helps the user place the carriage correctly. The machine has four rubber feet. At the back, two wooden cylinders have been attached to the base at the corners, so that the machine sits at an angle.

Plates attached to the right and left side read: MARCHANT. A metal plate right of the keyboard reads; MARCHANT (/) CALCULATORS (/) SIMPLICITY (/) ACCURACY (/) SPEED. A maker’s mark under the carriage on the right reads: 2097. A stamp on the bottom of the machine reads: KC 2097.

The Model KC, introduced in 1923 with initial serial number 1000, was one of Marchant Calculating Machine Company’s first three keyboard machines. It sold in 1924 for $350.00. By 1928 it was replaced by the model H-9.

Calvin Lieberman, the donor of this object, was associated with the steel recyling business in Toledo, Ohio, from at least 1937 through 1980.

This 92-page salmon-colored paperback book was received with 1981.0933.03. Its citation information is: William E. Breckenridge, The Polyphase Duplex Slide Rule: A Self Teaching Manual (New York: Keuffel & Esser Co., 1924). Breckenridge earned an A.M. in mathematics from Columbia University in New York City, was chair of the mathematics department at Stuyvesant High School around 1909–1910, served as an associate editor of The Mathematics Teacher from 1913 to 1928, and apparently also taught at Columbia.

Breckenridge explains the basic features and operations of the slide rule, discusses the history and theory of slide rules, provides methods for solving "advanced problems," treats plane trigonometry, solves triangle problems, and provides "typical examples relating to various occupations," such as secretarial work, excavation, and retail. Finally, he shows how to set the slide rule to solve various mechanical formulas and lists tables of equivalents for the basic C and D scales. In chapter one, a previous reader, presumably the donor, William J. Ellenberger, has checked off the examples and filled in the answers to the problems. An advertisement for K&E's other specialty and general slide rules appears at the back of the book. This manual sold for 50 cents.

A digitized copy of The Polyphase Duplex Slide Rule is available at http://sliderulemuseum.com/Manuals/M205_KE_PolyphaseDuplexSlideRule_4088-3_1924.pdf.

This 72-page salmon-colored paperback book was received with 1981.0933.03 and 1981.0933.05. Its citation information is: William Cox, The Mannheim (Polyphase) and the Duplex (Polyphase-Duplex) Slide Rules Complete Manual (New York: Keuffel & Esser Co., 1920). It sold for 50 cents. William Cox helped introduce the Mannheim slide rule to the United States, invented the duplex slide rule, and served as a mathematical consultant to Keuffel & Esser Company of New York, thus launching that firm into pioneering the American manufacture of slide rules. He first wrote this manual in 1891 and revised it in 1917, adding instructions for K&E's Polyphase Duplex slide rule (model 4088-3).

A notice inside the front cover explained how K&E had updated the Mannheim line (models 4031–4056) since Cox first wrote the manual. Cox thoroughly described the characteristics, operations, and scales of Mannheim and Polyphase (which was especially useful for problems involving powers or roots) slide rules. He provided a lengthy table of equivalents for the base scales, C and D, as well as methods for working out mechanical and other formulas. He then went through a similar discussion for the eight-inch Duplex rule (model 4065) and for the ten-inch Polyphase-Duplex rule (model 4088). A supplement by J. M. Willard of the State College of Pennsylvania addressed the solution of problems in plane trigonometry. Finally, there are advertisements for K&E's general and specialty slide rules, the frameless indicator patented in 1915, a magnifier, and surveying equipment.

This full-keyboard, printing adding machine has a steel frame painted black and green There are eight columns of color-coded black and white metal keys with digits written on paper and covered with clear plastic (the keys resemble those on early typewriters). Complementary digits are indicated on the keys. The total appears in eight glass-covered metal windows over number dials at the front of the machine. There are total and non-add keys left of the number keys and a repeat key on the right. The total key also clears the machine. A metal crank with a wooden handle on the right of the machine operates it. Behind the keyboard is a two-colored ribbon, printing mechanism, and fixed narrow carriage. There are nine type bars, eight for digits and one for special characters. There is a serrated edge for tearing off the paper tape.

The machine is marked on the front and behind the keyboard: VICTOR. It is marked on the back: PATENTED (/) JUNE 20,1919 - APRIL 13th,1920 (/) MFD. BY (/) VICTOR ADDING MACHINE CO. (/) CHICAGO, U.S.A. (/) OTHER PATENTS PENDING. The serial number, on a metal tag attached to the bottom of the machine, is 24843.

This adding machine was purchased in 1922 and used until 1982 by Samuel Bernstein in his capacity as Secretary-Treasurer of Wilner Branch 367 of Workmen’s Circle. Workmen’s Circle was a fraternal organization organized about 1900 to promote self-help among Jewish immigrants from Eastern Europe. Mr. Bernstein was 95 years old when he relinquished his position.